@jkristof MAME is the trickiest of all the emulators.
I'm not sure where you are finding your rom files, but there's not a single site that I can think of, where after the download, you would need to make it a zip file.
That's probably your first problem.
Second, if you are able to select a game, hold the A button to go into the menu options and change the emulator until the games works for you.
There's a few to choose from and many games only work on one specific emulator.
Also, using WinSCP is probably the easiest way to transfer files if you're using a Windows based computer.
https://winscp.net/eng/download.php
When using WinSCP, the default Username is: Raspberry
Password: Pi
To find your Raspberry's I.P. address, you can do that in the menu system when running Retropie.